A descent method for nonsmooth multiobjective optimization in hilbert spaces
The efficient optimization method for locally Lipschitz continuous multiobjective optimization problems from Gebken and Peitz (J Optim Theory Appl 188:696-723, 2021) is extended from finite-dimensional problems to general Hilbert spaces. The method iteratively computes Pareto critical points, where...
Gespeichert in:
| Hauptverfasser: | , , , , |
|---|---|
| Dokumenttyp: | Article (Journal) |
| Sprache: | Englisch |
| Veröffentlicht: |
12 September 2024
|
| In: |
Journal of optimization theory and applications
Year: 2024, Jahrgang: 203, Heft: 1, Pages: 455-487 |
| ISSN: | 1573-2878 |
| DOI: | 10.1007/s10957-024-02520-4 |
| Online-Zugang: | Verlag, kostenfrei, Volltext: https://doi.org/10.1007/s10957-024-02520-4
|
| Verfasserangaben: | Konstantin Sonntag, Bennet Gebken, Georg Müller, Sebastian Peitz, Stefan Volkwein |
MARC
| LEADER | 00000caa a2200000 c 4500 | ||
|---|---|---|---|
| 001 | 1917585772 | ||
| 003 | DE-627 | ||
| 005 | 20250716232721.0 | ||
| 007 | cr uuu---uuuuu | ||
| 008 | 250219s2024 xx |||||o 00| ||eng c | ||
| 024 | 7 | |a 10.1007/s10957-024-02520-4 |2 doi | |
| 035 | |a (DE-627)1917585772 | ||
| 035 | |a (DE-599)KXP1917585772 | ||
| 035 | |a (OCoLC)1528019162 | ||
| 040 | |a DE-627 |b ger |c DE-627 |e rda | ||
| 041 | |a eng | ||
| 084 | |a 27 |2 sdnb | ||
| 100 | 1 | |a Sonntag, Konstantin |e VerfasserIn |0 (DE-588)1356826792 |0 (DE-627)1917587333 |4 aut | |
| 245 | 1 | 2 | |a A descent method for nonsmooth multiobjective optimization in hilbert spaces |c Konstantin Sonntag, Bennet Gebken, Georg Müller, Sebastian Peitz, Stefan Volkwein |
| 264 | 1 | |c 12 September 2024 | |
| 300 | |b Illustrationen | ||
| 300 | |a 1-33$t33 | ||
| 336 | |a Text |b txt |2 rdacontent | ||
| 337 | |a Computermedien |b c |2 rdamedia | ||
| 338 | |a Online-Ressource |b cr |2 rdacarrier | ||
| 500 | |a Gesehen am 19.02.2025 | ||
| 520 | |a The efficient optimization method for locally Lipschitz continuous multiobjective optimization problems from Gebken and Peitz (J Optim Theory Appl 188:696-723, 2021) is extended from finite-dimensional problems to general Hilbert spaces. The method iteratively computes Pareto critical points, where in each iteration, an approximation of the Clarke subdifferential is computed in an efficient manner and then used to compute a common descent direction for all objective functions. To prove convergence, we present some new optimality results for nonsmooth multiobjective optimization problems in Hilbert spaces. Using these, we can show that every accumulation point of the sequence generated by our algorithm is Pareto critical under common assumptions. Computational efficiency for finding Pareto critical points is numerically demonstrated for multiobjective optimal control of an obstacle problem. | ||
| 650 | 4 | |a 34K35 | |
| 650 | 4 | |a 35B37 | |
| 650 | 4 | |a 49J52 | |
| 650 | 4 | |a 90C29 | |
| 650 | 4 | |a Descent methods in Hilbert spaces | |
| 650 | 4 | |a Multiobjective optimization | |
| 650 | 4 | |a Nonsmooth optimization | |
| 650 | 4 | |a Obstacle problem | |
| 650 | 4 | |a PDE-constrained optimization | |
| 700 | 1 | |a Gebken, Bennet |e VerfasserIn |4 aut | |
| 700 | 1 | |a Müller, Georg |d 1988- |e VerfasserIn |0 (DE-588)1172479798 |0 (DE-627)1041231857 |0 (DE-576)514647663 |4 aut | |
| 700 | 1 | |a Peitz, Sebastian |e VerfasserIn |0 (DE-588)1351488767 |0 (DE-627)1912955733 |4 aut | |
| 700 | 1 | |a Volkwein, Stefan |d 1966- |e VerfasserIn |0 (DE-588)118138529 |0 (DE-627)079266347 |0 (DE-576)178487201 |4 aut | |
| 773 | 0 | 8 | |i Enthalten in |t Journal of optimization theory and applications |d Dordrecht [u.a.] : Springer Science + Business Media, 1967 |g 203(2024), 1, Seite 455-487 |h Online-Ressource |w (DE-627)266883923 |w (DE-600)1468244-8 |w (DE-576)102668914 |x 1573-2878 |7 nnas |a A descent method for nonsmooth multiobjective optimization in hilbert spaces |
| 773 | 1 | 8 | |g volume:203 |g year:2024 |g number:1 |g pages:455-487 |g extent:1-33$t33 |a A descent method for nonsmooth multiobjective optimization in hilbert spaces |
| 856 | 4 | 0 | |u https://doi.org/10.1007/s10957-024-02520-4 |x Verlag |x Resolving-System |z kostenfrei |3 Volltext |
| 951 | |a AR | ||
| 992 | |a 20250219 | ||
| 993 | |a Article | ||
| 994 | |a 2024 | ||
| 998 | |g 1172479798 |a Müller, Georg |m 1172479798:Müller, Georg |d 700000 |d 708000 |e 700000PM1172479798 |e 708000PM1172479798 |k 0/700000/ |k 1/700000/708000/ |p 3 | ||
| 999 | |a KXP-PPN1917585772 |e 4666459987 | ||
| BIB | |a Y | ||
| SER | |a journal | ||
| JSO | |a {"name":{"displayForm":["Konstantin Sonntag, Bennet Gebken, Georg Müller, Sebastian Peitz, Stefan Volkwein"]},"origin":[{"dateIssuedDisp":"12 September 2024","dateIssuedKey":"2024"}],"id":{"eki":["1917585772"],"doi":["10.1007/s10957-024-02520-4"]},"physDesc":[{"extent":"1-33$t33 S.","noteIll":"Illustrationen"}],"relHost":[{"title":[{"title":"Journal of optimization theory and applications","title_sort":"Journal of optimization theory and applications"}],"pubHistory":["1.1967 -"],"part":{"year":"2024","pages":"455-487","issue":"1","text":"203(2024), 1, Seite 455-487","volume":"203","extent":"1-33$t33"},"disp":"A descent method for nonsmooth multiobjective optimization in hilbert spacesJournal of optimization theory and applications","note":["Gesehen am 01.11.05"],"type":{"media":"Online-Ressource","bibl":"periodical"},"recId":"266883923","language":["eng"],"origin":[{"publisherPlace":"Dordrecht [u.a.] ; New York, NY [u.a.] ; New York, NY [u.a.]","dateIssuedDisp":"1967-","dateIssuedKey":"1967","publisher":"Springer Science + Business Media ; Plenum Publ. Corp. ; Kluwer Acad./Plenum Publ."}],"id":{"zdb":["1468244-8"],"eki":["266883923"],"issn":["1573-2878"]},"physDesc":[{"extent":"Online-Ressource"}]}],"person":[{"given":"Konstantin","family":"Sonntag","role":"aut","roleDisplay":"VerfasserIn","display":"Sonntag, Konstantin"},{"role":"aut","display":"Gebken, Bennet","roleDisplay":"VerfasserIn","given":"Bennet","family":"Gebken"},{"role":"aut","roleDisplay":"VerfasserIn","display":"Müller, Georg","given":"Georg","family":"Müller"},{"display":"Peitz, Sebastian","roleDisplay":"VerfasserIn","role":"aut","family":"Peitz","given":"Sebastian"},{"roleDisplay":"VerfasserIn","display":"Volkwein, Stefan","role":"aut","family":"Volkwein","given":"Stefan"}],"title":[{"title_sort":"descent method for nonsmooth multiobjective optimization in hilbert spaces","title":"A descent method for nonsmooth multiobjective optimization in hilbert spaces"}],"note":["Gesehen am 19.02.2025"],"type":{"bibl":"article-journal","media":"Online-Ressource"},"recId":"1917585772","language":["eng"]} | ||
| SRT | |a SONNTAGKONDESCENTMET1220 | ||